iMac - weird problem with imac g4

Hi, hope you guys can help me out here. i have always been a pc guy but recently aquired a mac so im not too familiar with them. here's the deal, a guy gave me a 20" imac G4 and told me it had a bad mother board or something and that its a paper weight. i took it home and to my surprise i hit the power button and the thing worked absolutely perfectly for about a week. one day my 18 month old son was playing with it and i left the room and came back to see the computer was off and unplugged from the wall. i plugged it back in and tried to fire it up. i got the ding sound, the hard drive sound and all the other usuals except i had absolutely no display. i tried resetting it 10 times to no avail so i put it aside fro about a week. i plugged it in a week later and it worked perfect again so i unplugged it and took it to my desk where i plugged it in and again, everything powered up except the display. long story short, the display stops working sometimes when its turned off and will not come back on unless i put the computer aside for a week, and then it will work again. weird.

i have done a little research, i tried pressing the button under the base and it did nothing. when it powers on, there is no faint image at all so i dont think its the backlight. it is not a loose conection because when i get it to turn on i have knocked it all over the place and its been fine.

It would seem that it's a video card issue to me, but so odd that it works after a long rest, that makes no sense!
Do you have the install discs at all? I would run a hardware test to see if it shows up anything. You could also zap PRAM and reset NVRAM to see if that helps (especially NVRAM reset).
If you need to know how there are instructions in my post here: